Question

What is the solution for the system of equations?

y=2x−3


4x−3y=31


(2 points)
The solution to the system is (
,
)

Answer 1

To solve the system of equations, we have:

1. \( y = 2x - 3 \) (Equation 1)
2. \( 4x - 3y = 31 \) (Equation 2)

We can use Equation 1 to substitute for \( y \) in Equation 2.

Substituting \( y \) in Equation 2:

\[
4x - 3(2x - 3) = 31
\]

Now, simplify the equation:

\[
4x - 6x + 9 = 31
\]

Combine like terms:

\[
-2x + 9 = 31
\]

Now, isolate \( x \):

\[
-2x = 31 - 9
\]
\[
-2x = 22
\]
\[
x = -11
\]

Now, substitute \( x = -11 \) back into Equation 1 to find \( y \):

\[
y = 2(-11) - 3
\]
\[
y = -22 - 3
\]
\[
y = -25
\]

So the solution to the system of equations is:

\((-11, -25)\)

Thus, the solution to the system is \((-11, -25)\).